For the parametrisation, think in terms of polar coordinates. The equation of the curve reduces to . But that is a bit problematical, because can be negative. A possible parametrisation would be, where
and .

That doesn't look like a good solution, because of the unpleasant singularity at the origin. The curve looks like an symbol, and that parametrisation describes both loops in the same (anticlockwise) direction. It would be much better to have a parametrisation that went straight across the origin without stopping there, so as to go anticlockwise round the right loop and clockwise round the left loop. But as far as I can see, there is no simple formula for such a description of the curve.